Question

A parabola, which is given by the equation y = x^(2)+ax+b, attains its minimum at (6,8). Find a and b.
a =
b =

Answer 1

y = x^2 + ax + b
(6,8) lies on it, so 8 = 36 + 6a + b
6a + b = -28

dy/dx = 2x + a
when x = 6, the dy/dx = 0
2(6) + a = 0
a = -12

Answer 2

The vertex is at (6,8) so the equation is
y = m(x-6)^2 + 8 = mx^2 - 12mx + 36m+8
m=1, so
a = -12
b = 44